A Minimally-biased Philosophy of Life: Structure of a Grand Unified Theory

Feynman got to characterize physical law, so let me caricature him. He said that the best physical laws are the simplest and the most multi-scale, like 1/r^2 for gravitation and electrostatics, e = mc^2, Newton's Laws, and the laws of thermodynamics. The advantages Feynman appealed to in equations are those also used for information compression: the more phenomena and scale are compressed into the smallest expression with the fewest discontinuities, the better the compression ratio. For example, E=mc^2 is a whole universe of description packed into six bytes. In other words, the best laws please both Bayes and Occam. For me, and perhaps for Feynman, universal physical theories are perhaps the most hyper-compressed structures possible in the universe.

Physicists use the phrase Grand Unified Theory to describe such claims. Below we will discuss the necessary structure for such theories to take (the "meta-theory," if you will). But first, the evaluation process.

How is an intellectually honest person to judge a new Grand Unified Theory on the few occasions one comes around? A theorist would be tempted to invoke all manner of high-flown theoretic qualifications for a deserving Grand Theory, but such recommendations might be deemed self-interested. So here's a practical suggestion first: ask if it makes sense and seems easy to apply. Any grand theory worth its salt should be clear and coherent on the face of it, and should have practical, immediate consequences which are easy to check. If you can't self-validate it in your own life pretty quickly, it's not much use anyway.

Formally, one should evaluate any Grand Unified Theory according to the unique intellectual advantage it claims, the same one praised by Feynman: its continuity across all space and time. For a theory of humanity, that means its continuity across disciplines and human history. The best we can hope for is that a new Grand Unified Theory accords with the most elemental tenets of enough principled disciplines to signal its overall coherence, and yet disagrees with (or points out moral hazards in) other disciplines according to bias introduced by socially challenging subject matter. In other words, a Grand Unified Theory absolutely must agree with math, computer science, and most of physics, whereas disagreement with aspects of psychology, political theory, and economics is also nearly guaranteed.

Self-consistency and coherence are all any Grand Theory could possibly provide upon first introduction ; completeness comes over time. It must treat each discipline coarsely, at first, to avoid possible confusion in translation later on. But by current publishing standards, this breadth-first approach makes it difficult to defend at the level of detail and knowledge any particular discipline usually expects. Furthermore, few individuals feel qualified to evaluate intellectual coherence on such a wide scale. So the same social and economic pressures which limit grand theorists also limit avenues to validate their work.

I felt the personal sting of these impersonal pressures when a grad student. I had submitted to a major journal the most compact paper I could imagine: two paragraphs, one simple equation, one simple figure, with a conclusion that subsequently spawned research programs and careers. But both referees rejected it. One asserted my conclusion was too obvious to publish; the other said I was flat-out wrong. Unfortunately, they did agree one one thing: the paper should not be published. In this case, as in any competitive environment, disapproval sums coherently, even if its justifications are incoherent and thus collectively unjustified. Grand Unified Theories also face coherent disapproval and systematic when they compete with existing explanatory systems; in fact, an ideal theory which explains everything would thereby threaten significant tenets of every discipline it subsumes.

The structure of the theory

This theory is self-similar: it proposes that brains use a multiscale continuous representational structure, and itself has such a structure, because the theory's claims overlap and cohere across disciplines. The coherence, in fact, provides the theory's strength strength, like a crystal except even stronger. Let me illustrate.

Physicists know that one-dimensional crystals can exist, along with two- and three-dimensional ones. They also know that structural stability increases with dimension: 1-D crystals often won't crystallize at all, and 2-D ones only under special circumstances. Only 3-D crystals are truly solid, because the additional dimensions allow further correlations which give it strength. If a crystal could be made with more than three dimensions--i.e. a hyper-crystal--it would be hyper-stable.

A Grand Unified Theory is like a hyper-dimensional data-space, which in turn is like a hyper-crystal. Focused views of a data space (called "slices", as with MRI scans) can be taken along many axes, each giving orthogonal information. For a Grand Unified Theory, the lensing or slicing occurs along conceptual axes rather than numerical or physical ones, but the structural impact is the same: the more independent directions along which the material can be analzyed coherently, the stronger is the underlying theory.

[picture of all-to-all nodes vs. multi-tree structure goes here]

This is why a web-site is the perfect display format for a Grand Unified Theory. The inhernet all-to-all connections of the concepts can be arranged as overlapping directed trees, each "lens" of interpretation mapping to one root node of one tree. Those lens-nodes can in turn be assembled under a single node, the entrance portal to the site. Hyperlinks connecting nodes and concepts serve like cross-links in a polymer, tightening the overall structure and providing yet more paths for navigating the theory in any direction the viewer wants.

The structural challenge is that a Grand Unified theory is a formally static structure with possibly dozens of latent dimensions, while a human viewer at any given time can only navigate a single, one-dimensional narrative path through it. If the theory were expressed in linear order, as in a scientific paper, after experiencing that single path a viewer would have to reconstruct from it the original multi-dimensional structure in her head. That's hard. Here we try an easier approach: display the entire theory into its native multi-dimensional format, and let the viewer discover that multi-dimensionality by exploring it serially on her own terms.